A criticism I hate getting from readers is that I have made a character do something that really doesn't make sense, given their personality. This always makes me defensive. After all, I created the character. I should know her, it, or him better than anyone else. And, most likely, I do know the character better than anyone else, and she, it, or he would do something like that...I just didn't make that clear in the story.
What this comes down to (and Yat-Yee describes this well) is that readers are experiencing our characters in the sequence of the story, whereas we writers have the luxury of seeing all of the material that happens throughout our character's lifetimes, not just what's on the page. So, how can we provide these clues to our reader before they feel betrayed?
That's where the first impression comes in. As readers are discovering each character in our story, they are comparing them with one another, with real people in their lives, and probably with themselves. And, because most people attempt to understand things as soon as possible, they create judgments based on the first impressions.
If readers get three consecutive scenes where Albert is afraid of water, they will be suspicious if Albert suddenly dives off the pier to save is alien boyfriend from drowning. But, if Albert's first three scenes include one where he refuses to go into the water, one where he jumps cautiously into the deep end of the pool, and one where he sits on the edge of the pool with his feet dangling in the water, we're not quite as sure of what he'll do next. He may be willing to save Sbortfa'an, or he may have to hope that Sbortfa'an's alien family is nearby to do the saving for him...and that they aren't allergic to water. Albert now has a larger dynamic range with which we can work with.
If you want to have a character who is capable of performing a wider range of actions, I think you have to hint at the character's full range of possibilities early on, especially during those beginning pages where readers are shaping their first impressions of the character (the first 17 pages, to be exact*). If we establish absolute personality traits for a character, then I think we have to accept that they are going to stay that way unless some external force comes in later on to change them (and, naturally, this is one great way to develop a character).
Now, of course, this can work both ways. If we are systematic and plan ahead, if we know what we want our characters to do at the end before we have written the beginning, then we can plant the seeds to show what they are capable of. But, hopefully, the reader's experience will be the same whether we plan this forwards or backwards. Either way, we don't want to limit our characters' range unless that limitation is something that will help us later on.
Strange combinations of character traits can help us with this wide dynamic range. The example I've used before is Brod from Jonathan Safran Foer's book Everything Is Illuminated. Brod is an orphan girl in a Jewish town, and every man (and a few women) are desperately attracted to her. Yet, Foer describes Brod is short and skinny, to the point of looking perpetually sick. These are not traits that we usually associate with attractiveness, and because of that, Foer is able to create a character who is capable of more. She's both ugly and attractive at the same time. Foer hasn't committed her to being one or the other.
So, when sending your characters along their story trajectories, make sure you reveal their whole range of capabilities. Trapping them into a single personality type often means that you'll have to rely on an external force to change the character or do the character's work later on.
*Yes, it's 17 pages. Decades of scientific evidence have proven this without a doubt. Without a doubt!